Solve the Fraction Addition: 4/10 + 5/12 Step-by-Step

Fraction Addition with Unlike Denominators

Solve the following equation:

410+512= \frac{4}{10}+\frac{5}{12}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Multiply each fraction by 6 and 4 respectively to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:16 Calculate the multiplications
00:29 Add with the common denominator
00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

410+512= \frac{4}{10}+\frac{5}{12}=

2

Step-by-step solution

Let's first identify the lowest common denominator between 10 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 10 and 12.

In this case, the common denominator is 60.

We'll proceed to multiply each fraction by the appropriate number to reach the denominator 60.

We'll multiply the first fraction by 6

We'll multiply the second fraction by 5

4×610×6+5×512×5=2460+2560 \frac{4\times6}{10\times6}+\frac{5\times5}{12\times5}=\frac{24}{60}+\frac{25}{60}

Now let's add:

24+2560=4960 \frac{24+25}{60}=\frac{49}{60}

3

Final Answer

4960 \frac{49}{60}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find the least common multiple of both denominators
  • Technique: Multiply 410 \frac{4}{10} by 6 and 512 \frac{5}{12} by 5 to get 60
  • Check: Verify 2460+2560=4960 \frac{24}{60} + \frac{25}{60} = \frac{49}{60} cannot simplify further ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 4+5=9 and 10+12=22 to get 9/22! This ignores that fractions represent parts of different-sized wholes. Always find the LCD first and convert both fractions to equivalent fractions with the same denominator.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

Why can't I just add 4/10 + 5/12 directly?

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You can't add fractions with different denominators because they represent parts of different-sized wholes. It's like trying to add 4 slices of a 10-piece pizza to 5 slices of a 12-piece pizza - you need a common reference first!

How do I find the LCD of 10 and 12?

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List the multiples of each number: 10: 10, 20, 30, 40, 50, 60... 12: 12, 24, 36, 48, 60... The first number that appears in both lists is 60, so that's your LCD!

What numbers do I multiply each fraction by?

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Divide the LCD by each denominator: 60 ÷ 10 = 6 and 60 ÷ 12 = 5. So multiply the first fraction by 6/6 and the second by 5/5.

Can I simplify 49/60 further?

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No! Since 49 = 7 × 7 and 60 = 2² × 3 × 5, they share no common factors. The fraction 4960 \frac{49}{60} is already in lowest terms.

What if I got a different LCD like 120?

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While 120 works (it's divisible by both 10 and 12), it's not the least common denominator. You'd get 98120 \frac{98}{120} , which simplifies back to 4960 \frac{49}{60} anyway!

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